Skip to main content
SpringerLink
Log in

New Approach for Interpretability of Neuro-Fuzzy Systems with Parametrized Triangular Norms

  • Conference paper
  • First Online:
Artificial Intelligence and Soft Computing (ICAISC 2016)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9692))

Included in the following conference series:

Abstract

In this paper we proposed a new approach for interpretability of the neuro-fuzzy systems. It is based on appropriate use of parametric triangular norms with weights of arguments, which shape depends on values of their parameters and weights. The use of those norms as aggregation and inference operators increases precision of fuzzy system. Due to that, the rule base can be simpler and easier to interpretation. However, interpretation of parametric triangular norms is not that obvious as interpretation of nonparametric triangular norms such as algebraic or minimal norms. Proposed approach is based on choosing values of parameters from a set of values, where each value have its own interpretation. Additionally, a modified tuning algorithm for selection both the structure and structure parameters of fuzzy system with interpretability criteria under consideration is proposed. Proposed approach were tested on well-known nonlinear simulation problems.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Abbas, J.: The bipolar Choquet integrals based on ternary-element sets. J. Artif. Intell. Soft Comput. Res. 6(1), 13–21 (2016)

    Article  Google Scholar 

  2. Alcal, R., Ducange, P., Herrera, F., Lazzerini, B., Marcelloni, F.: A multi-objective evolutionary approach to concurrently learn rule and data base sof linguistic fuzzy rule-based systems. IEEE Trans. Fuzzy Syst. 17, 1106–1122 (2009)

    Article  Google Scholar 

  3. Alonso J. M.: Modeling Highly Interpretable Fuzzy Systems, European Centre for Soft Computing (2010)

    Google Scholar 

  4. Alonso, J.M., Magdalena, L.: HILK++: an interpretability-guided fuzzy modeling methodology for learning readable and comprehensible fuzzy rule-based classifiers. Soft Computing 15(10), 1959–1980 (2011)

    Article  Google Scholar 

  5. Bartczuk, Ł.: Gene expression programming in correction modelling of nonlinear dynamic objects. Adv. Intell. Syst. Comput. 429, 125–134 (2016)

    Article  Google Scholar 

  6. Bartczuk, Ł., Przybył, A., Koprinkova-Hristova, P.: New method for nonlinear fuzzy correction modelling of dynamic objects. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2014, Part I. LNCS, vol. 8467, pp. 169–180. Springer, Heidelberg (2014)

    Chapter  Google Scholar 

  7. Bartczuk, Ł., Rutkowska, D.: Type-2 fuzzy decision trees. In: Rutkowski, L., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2008. LNCS (LNAI), vol. 5097, pp. 197–206. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  8. Bartczuk, Ł., Rutkowska, D.: Medical diagnosis with type-2 fuzzy decision trees, computers in medical activity. Adv. Intell. Soft Comput. 65, 11–21 (2009)

    Article  Google Scholar 

  9. Bruździński, T., Krzyżak, A., Fevens, T., Jeleń, Ł.: Web-based framework for breast cancer classification. J. Artif. Intell. Soft Comput. Res. 4(2), 149–162 (2014)

    Google Scholar 

  10. Cheng, Y.I.: Modeling slump flow of concrete using second-order regressions and artificial neural networks. CCC 29(6), 474–480 (2007)

    Article  Google Scholar 

  11. Cierniak, R., Rutkowski, L.: On image compression by competitive neural networks and optimal linear predictors. Signal Process. Image Commun. 156, 559–565 (2000)

    Article  Google Scholar 

  12. Cpalka, K.: A method for designing flexible neuro-fuzzy systems. In: Rutkowski, L., Tadeusiewicz, R., Zadeh, L.A., Żurada, J.M. (eds.) ICAISC 2006. LNCS (LNAI), vol. 4029, pp. 212–219. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  13. Cpałka, K.: A new method for design and reduction of neuro-fuzzy classification systems. IEEE Trans. Neural Networks 20, 701–714 (2009)

    Article  Google Scholar 

  14. Cpałka, K.: On evolutionary designing and learning of flexible neuro-fuzzy structures for nonlinear classification. Nonlinear Anal. Series A. Theor. Methods Appl. 71(2009), e1659–e1672 (2009). Elsevier

    Google Scholar 

  15. Cpałka, K., Łapa, K., Przybył, A., Zalasiński, M.: A new method for designing neuro-fuzzy systems for nonlinear modelling with interpretability aspects. Neurocomput. 135, 203–217 (2014)

    Article  Google Scholar 

  16. Cpałka, K., Rebrova, O., Nowicki, R., Rutkowski, L.: On design of flexible neuro-fuzzy systems for nonlinear modelling. Int. J. General Syst. 42(6), 706–720 (2013)

    Article  MATH  Google Scholar 

  17. Cpałka, K., Rutkowski, L.: Flexible Takagi-Sugeno neuro-fuzzy structures for nonlinear approximation. WSEAS Trans. Syst. 4(9), 1450–1458 (2005)

    Google Scholar 

  18. Cpałka K., Rutkowski L.: Flexible Takagi-Sugeno fuzzy systems, Neural Networks. In: Proceedings of the 2005 IEEE International Joint Conference on IJCNN 2005, vol. 3, pp. 1764–1769 (2005)

    Google Scholar 

  19. Cpałka, K., Zalasiński, M.: On-line signature verification using vertical signature partitioning. Expert Syst. Appl. 41(9), 4170–4180 (2014)

    Article  Google Scholar 

  20. Cpałka, K., Zalasiński, M., Rutkowski, L.: New method for the on-line signature verification based on horizontal partitioning. Pattern Recogn. 47, 2652–2661 (2014)

    Article  Google Scholar 

  21. Cpałka, K., Zalasiński, M., Rutkowski, L.: A new algorithm for identity verification based on the analysis of a handwritten dynamic signature. Appl. Soft Comput. 43, 47–56 (2016)

    Article  Google Scholar 

  22. Das, S., Kar, S., Pal, T.: Group decision making using interval-valued intuitionistic fuzzy soft matrix and confident weight of experts. J. Artif. Intell. Soft Comput. Res. 4(1), 57–77 (2014)

    Article  Google Scholar 

  23. Duda, P., Hayashi, Y., Jaworski, M.: On the Strong convergence of the orthogonal series-type kernel regression neural networks in a non-stationary environment. In: Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M., Rutkowski, L. (eds.) ICAISC 2012, Part I. LNCS, vol. 7267, pp. 47–54. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  24. Duda, P., Jaworski, M., Pietruczuk, L.: On pre-processing algorithms for data stream. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2012, Part II. LNCS, vol. 7268, pp. 56–63. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  25. Dziwiński, P., Avedyan, E.D.: A new approach to nonlinear modeling based on significant operating points detection. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2015. LNCS, vol. 9120, pp. 364–378. Springer, Heidelberg (2015)

    Chapter  Google Scholar 

  26. Dziwiński, P., Bartczuk, Ł., Przybył, A., Avedyan, E.D.: A new algorithm for identification of significant operating points using swarm intelligence. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2014, Part II. LNCS, vol. 8468, pp. 349–362. Springer, Heidelberg (2014)

    Chapter  Google Scholar 

  27. Er, M.J., Duda, P.: On the weak convergence of the orthogonal series-type kernel regresion neural networks in a non-stationary environment. In: Wyrzykowski, R., Dongarra, J., Karczewski, K., Waśniewski, J. (eds.) PPAM 2011, Part I. LNCS, vol. 7203, pp. 443–450. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  28. Farahbod, F., Eftekhari, M.: Comparsion of different T-norm operators in classification problems. Int. J. Fuzzy Logic Syst. 2(3), 33–41 (2012)

    Article  Google Scholar 

  29. Gabryel, M., Cpałka, K., Rutkowski, L.: Evolutionary strategies for learning of neuro-fuzzy systems. In: Proceeding of the I Workshop on Genetic Fuzzy Systems, Granada, pp. 119–123 (2005)

    Google Scholar 

  30. Gabryel, M., Korytkowski, M., Scherer, R., Rutkowski, L.: Object detection by simple fuzzy classifiers generated by boosting. In: Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M., Rutkowski, L. (eds.) ICAISC 2013, Part I. LNCS, vol. 7894, pp. 540–547. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  31. Gacto, M.J., Alcal, R., Herrera, F.: Integration of an index to preserve the semantic interpretability in the multi-objective evolutionary rule selection and tuning of linguistic fuzzy systems. IEEE Trans. Fuzzy Syst. 18, 515–531 (2010)

    Article  Google Scholar 

  32. Gacto, M.J., Alcal, R., Herrera, F.: Interpretability of linguistic fuzzy rule-based systems: an overview of interpretability measures. Inf. Sci. 181(20), 4340–4360 (2011)

    Article  Google Scholar 

  33. Gałkowski, T., Rutkowski, L.: Nonparametric recovery of multivariate functions with applications to system identification. Proc. IEEE 73(5), 942–943 (1985)

    Article  Google Scholar 

  34. Grycuk, R., Gabryel, M., Korytkowski, M., Scherer, R., Voloshynovskiy, S.: From single image to list of objects based on edge and blob detection. In: Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M., Rutkowski, L. (eds.) ICAISC 2014, Part II. LNCS, vol. 8468, pp. 605–615. Springer, Heidelberg (2014)

    Chapter  Google Scholar 

  35. Guillaume, S., Charnomordic, B.: Generating an interpretable family of fuzzy partitions from data. IEEE Trans. Fuzzy Syst. 12(3), 324–335 (2004)

    Article  Google Scholar 

  36. Icke, I., Rosenberg, A.: Multi-objective genetic programming for visual analytics. In: Silva, S., Foster, J.A., Nicolau, M., Machado, P., Giacobini, M. (eds.) EuroGP 2011. LNCS, vol. 6621, pp. 322–334. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  37. Ishibuchi, H., Nakashima, T., Murata, T.: Comparsion of the Michigan and Pittsburgh approaches to the design of fuzzy classification systems. Electr. Commun. Japan, Part 3 80(12), 379–387 (1997)

    Google Scholar 

  38. Ishibuchi, H., Nojima, Y.: Analysis of interpretability-accuracy tradeoff of fuzzy systems by multiobjective fuzzy genetics-based machine learning. Int. J. Approximate Reasoning 44, 4–31 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  39. Jaworski, M., Er, M.J., Pietruczuk, L.: On the application of the parzen-type kernel regression neural network and order statistics for learning in a non-stationary environment. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2012, Part I. LNCS, vol. 7267, pp. 90–98. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  40. Jaworski, M., Pietruczuk, L., Duda, P.: On resources optimization in fuzzy clustering of data streams. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2012, Part II. LNCS, vol. 7268, pp. 92–99. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  41. Kitajima, R., Kamimura, R.: Accumulative information enhancement in the self-organizing maps and its application to the analysis of mission statements. J. Artif. Intell. Soft Comput. Res. 5(3), 161–176 (2015)

    Article  Google Scholar 

  42. Korytkowski, M., Nowicki, R., Scherer, R.: Neuro-fuzzy rough classifier ensemble. In: Alippi, C., Polycarpou, M., Panayiotou, C., Ellinas, G. (eds.) ICANN 2009, Part I. LNCS, vol. 5768, pp. 817–823. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  43. Korytkowski, M., Rutkowski, L., Scherer, R.: From ensemble of fuzzy classifiers to single fuzzy rule base classifier. In: Rutkowski, L., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2008. LNCS (LNAI), vol. 5097, pp. 265–272. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  44. Korytkowski, M., Rutkowski, L., Scherer, R.: Fast image classification by boosting fuzzy classifiers. Inf. Sci. 327, 175–182 (2016)

    Article  MathSciNet  Google Scholar 

  45. Kummer, N., Najjaran, H.: Adaboost.MRT: boosting regression for multivariate estimation. Artif. Intell. Res. 3(4), 64–76 (2014)

    Article  Google Scholar 

  46. Laskowski, Ł., Laskowska, M.: Probing of synthesis route. J. Solid State Chem. 220, 221–226 (2014)

    Article  Google Scholar 

  47. Laskowski, Ł., Laskowska, M., Bałanda, M., Fitta, M., Kwiatkowska, J., Dziliński, K., Karczmarska, A.: Raman and magnetic analysis. Microporous Mesoporous Mater. 200, 253–259 (2014)

    Article  Google Scholar 

  48. Li, X., Er, M.J., Lim, B.S., Zhou, J.H., Gan, O.P., Rutkowski, L.: Fuzzy regression modeling for tool performance prediction and degradation detection. Int. J. Neural Syst. 2005, 405–419 (2010)

    Article  Google Scholar 

  49. Liu, F., Quek, C., Ng, G.S.: A novel generic hebbian ordering-based fuzzy rule base reduction approach to Mamdani neuro-fuzzy system. Neural Comput. 19, 1656–1680 (2007)

    Article  MATH  Google Scholar 

  50. Ludwig, S.A.: Repulsive self-adaptive acceleration particle swarm optimization approach. J. Artif. Intell. Soft Comput. Res. 4(3), 189–204 (2014)

    Article  Google Scholar 

  51. Łapa K.: Algorithms for extracting interpretable expert knowledge in nonlinear modeling issues, PhD Thesis (in polish), Czestochowa University of Technology (2015)

    Google Scholar 

  52. Łapa, K., Przybył, A., Cpałka, K.: A new approach to designing interpretable models of dynamic systems. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2013, Part II. LNCS, vol. 7895, pp. 523–534. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  53. Łapa, K., Zalasiński, M., Cpałka, K.: A new method for designing and complexity reduction of neuro-fuzzy systems for nonlinear modelling. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2013, Part I. LNCS, vol. 7894, pp. 329–344. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  54. Marquez A. A., Marquez F. A., Peregrin A.: A multi-objective evolutionary algorithm with an interpretability improvement mechanism for linguistic fuzzy systems with adaptive defuzzification. In: IEEE International Conference on Fuzzy Systems, pp. 1–7 (2010)

    Google Scholar 

  55. Mencar, C., Castellano, G., Fanelli, A.M.: On the role of interpretability in fuzzy data mining. Int. J. Uncertainty Fuzziness Knowl. Based Syst. 15(5), 521–537 (2007)

    Article  MATH  Google Scholar 

  56. Mencar, C., Castiello, C., Cannone, R., Fanelli, A.M.: Interpretability assessment of fuzzy knowledge bases: a cointension based approach. Int. J. Approximate Reasoning 52(4), 501–518 (2011)

    Article  MathSciNet  Google Scholar 

  57. Nelson, W.: Analysis of performance-degradation data. IEEE Trans. Reliab. 2(2), 149–155 (1981)

    Article  MATH  Google Scholar 

  58. Nobukawa, S., Nishimura, H., Yamanishi, T., Liu, J.-Q.: Chaotic states induced by resetting process in Izhikevich Neuron Model. J. Artif. Intell. Soft Comput. Res. 5(2), 109–119 (2015)

    Article  Google Scholar 

  59. Ortigosa I., Lopez R., Garcia J.: A neural networks approach to residuary resistance of sailing yachts prediction. In: Proceedings of the International Conference on Marine Engineering MARINE 2007 (2007)

    Google Scholar 

  60. Osaba, E.: Golden Ball: a novel meta-heuristic to solve combinatorial optimization problems based on soccer concepts. Appl. Intell. 12(2013), 145–166 (2013)

    Google Scholar 

  61. Patgiri, C., Sarma, M., Sarma, K.K.: A class of neuro-computational methods for assamese fricative classification. J. Artif. Intell. Soft Comput. Res. 5(1), 59–70 (2015)

    Article  Google Scholar 

  62. Pietruczuk, L., Duda, P., Jaworski, M.: A new fuzzy classifier for data streams. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2012, Part I. LNCS, vol. 7267, pp. 318–324. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  63. Pietruczuk, L., Duda, P., Jaworski, M.: Adaptation of decision trees for handling concept drift. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2013, Part I. LNCS, vol. 7894, pp. 459–473. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  64. Pulkkinen, P., Koivisto, H.: A dynamically constrained multiobjective genetic fuzzy system for regression problems. IEEE Trans. Fuzzy Syst. 18(1), 161–177 (2010)

    Article  Google Scholar 

  65. Riid, A., Rüstern, E.: Interpretability, interpolation and rule weights in linguistic fuzzy modeling. In: Fanelli, A.M., Pedrycz, W., Petrosino, A. (eds.) WILF 2011. LNCS, vol. 6857, pp. 91–98. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  66. Rutkowska, A.: Influence of membership functions shape on portfolio optimization results. J. Artif. Intell. Soft Comput. Res. 6(1), 45–54 (2016)

    Article  Google Scholar 

  67. Rutkowski, L.: Identification of MISO nonlinear regressions in the presence of a wide class of disturbances. IEEE Trans. Inform. Theory 37(1), 214–216 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  68. Rutkowski, L., Cpaka, K.: Flexible neuro fuzzy systems. IEEE Trans. Neural Networks 14, 554–574 (2003)

    Article  Google Scholar 

  69. Rutkowski, L.: Adaptive probabilistic neural networks for pattern classification in time-varying environment. IEEE Trans. Neural Networks 15(4), 811–827 (2004)

    Article  MathSciNet  Google Scholar 

  70. Rutkowski, L.: Flexible Neuro-Fuzzy Systems. Kluwer Academic Publishers, Dordrecht (2004)

    MATH  Google Scholar 

  71. Rutkowski, L.: Computational Intelligence. Springer, Heidelberg (2008)

    Book  MATH  Google Scholar 

  72. Rutkowski, L., Cpałka, K.: Flexible structures of neuro-fuzzy systems. In: Sincak, P., Vascak, J. (eds.) Quo Vadis Computational Intelligence. Studies in Fuzziness and Soft Computing, vol. 54, pp. 479–484. Springer, Heidelberg (2000)

    Google Scholar 

  73. Rutkowski, L., Cpałka, K.: Compromise approach to neuro-fuzzy systems. In: Sincak, P., Vascak, J., Kvasnicka, V., Pospichal, J. (eds.) Intelligent Technologies - Theory and Applications, vol. 76, pp. 85–90. IOS Press (2002)

    Google Scholar 

  74. Rutkowski L., Cpałka K.: Flexible weighted neuro-fuzzy systems. In: Proceedings of the 9th Internationa; Conference on Neural Information Processing (ICONIP-02), Orchid Country Club, Singapore, 18–22 November 2002. CD

    Google Scholar 

  75. Rutkowski L., Cpałka K.: Neuro-fuzzy systems derived from quasi-triangular norms. In: Proceedings of the IEEE International Conference on Fuzzy Systems, Budapest, 26–29 July 2004, vol. 2, pp. 1031–1036 (2004)

    Google Scholar 

  76. Rutkowski, L., Jaworski, M., Pietruczuk, L., Duda, P.: Decision trees for mining data streams based on the gaussian approximation. IEEE Trans. Knowl. Data Eng. 26(1), 108–119 (2014)

    Article  Google Scholar 

  77. Rutkowski, L., Jaworski, M., Pietruczuk, L., Duda, P.: The CART decision tree for mining data streams. Inf. Sci. 266, 1–15 (2014)

    Article  Google Scholar 

  78. Rutkowski, L., Pietruczuk, L., Duda, P., Jaworski, M.: Decision Trees for mining data streams based on the McDiarmid’s bound. IEEE Trans. Knowl. Data Eng. 25(6), 1272–1279 (2013)

    Article  Google Scholar 

  79. Rutkowski, L., Przybył, A., Cpałka, K., Er, M.J.: Online speed profile generation for industrial machine tool based on neuro-fuzzy approach. In: Rutkowski, L., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2010, Part II. LNCS, vol. 6114, pp. 645–650. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  80. Scherer, R.: Neuro-fuzzy systems with relation matrix. In: Rutkowski, L., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2010, Part I. LNCS, vol. 6113, pp. 210–215. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  81. Scherer R., Rutkowski L.: Relational equations initializing neuro-fuzzy system. In: Proceeding of the 10th Zittau Fuzzy Colloquium, Zittau, Germany, pp. 18–22 (2002)

    Google Scholar 

  82. Shukla, P.K., Tripathi, S.P.: A new approach for tuning interval type-2 fuzzy knowledge bases using genetic algorithms. J. Uncertainty Anal. Appl. 2(4), 1–15 (2014)

    MathSciNet  Google Scholar 

  83. Starczewski, J.T., Bartczuk, Ł., Dziwiński, P., Marvuglia, A.: Learning methods for type-2 FLS based on FCM. In: Rutkowski, L., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2010, Part I. LNCS, vol. 6113, pp. 224–231. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  84. Szarek, A., Korytkowski, M., Rutkowski, L., Scherer, R., Szyprowski, J.: Application of neural networks in assessing changes around implant after total hip arthroplasty. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2012, Part II. LNCS, vol. 7268, pp. 335–340. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  85. Szarek, A., Korytkowski, M., Rutkowski, L., Scherer, R., Szyprowski, J.: Forecasting wear of head and acetabulum in hip joint implant. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2012, Part II. LNCS, vol. 7268, pp. 341–346. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  86. Szczypta, J., Przybył, A., Cpałka, K.: Some aspects of evolutionary designing optimal controllers. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2013, Part II. LNCS, vol. 7895, pp. 91–100. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  87. Szczypta, J., Przybył, A., Wang, L.: Evolutionary approach with multiple quality criteria for controller design. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2014, Part I. LNCS, vol. 8467, pp. 455–467. Springer, Heidelberg (2014)

    Chapter  Google Scholar 

  88. Smyczyńska, J., Hilczer, M., Smyczyńska, U., Stawerska, R., Tadeusiewicz, R., Lewiński, A.: Artificial neural models - a novel tool for predictying the efficacy of growth hormone (GH) therapy in children with short stature. Neuroendocrinology Lett. 36(4), 348–353 (2015). (ISSN: 0172-780X, ISSN-L: 0172-780X)

    Google Scholar 

  89. Smyczyńska, U., Smyczyńska, J., Hilczer, M., Stawerska, R., Lewiński, A.: Artificial neural networks - a novel tool in modelling the effectiveness of growth hormone (GH) therapy in children with GH deficiency. Pediatric Endocrinology 14(2(51)), 9–18 (2015)

    Article  Google Scholar 

  90. Tadeusiewicz, R.: Neural networks as a tool for modeling of biological systems. Bio-Algorithms Med-Syst. 11(3), 135–144 (2015)

    Google Scholar 

  91. Tadeusiewicz, R.: Neural networks in mining sciences - general overview and some representative examples. Archivum Min. Sci. 60(4), 971–984 (2015)

    Google Scholar 

  92. Vanhoucke, V., Silipo, R.: Interpretability in multidimensional classification. In: Casillas, J., Cordón, O., Herrera, F., Magdalena, L. (eds.) Interpretability Issues in Fuzzy Modeling. Studies in Fuzziness and Soft Computing, vol. 128, pp. 193–217. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  93. Yamamoto, Y., Yoshikawa, T., Furuhashi, T.: Improvement of performance of Japanese P300 speller by using second display. J. Artif. Intell. Soft Comput. Res. 5(3), 221–226 (2015)

    Article  Google Scholar 

  94. Zalasiński M., Cpałka K.: A new method of on-line signature verification using a flexible fuzzy one-class classifier, pp. 38–53. Academic Publishing House EXIT (2011)

    Google Scholar 

  95. Zalasiński, M., Cpałka, K.: New approach for the on-line signature verification based on method of horizontal partitioning. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2013, Part II. LNCS, vol. 7895, pp. 342–350. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  96. Zalasiński, M., Cpałka, K., Er, M.J.: New method for dynamic signature verification using hybrid partitioning. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2014, Part II. LNCS, vol. 8468, pp. 216–230. Springer, Heidelberg (2014)

    Chapter  Google Scholar 

  97. Zalasiński, M., Cpałka, K., Er, M.J.: A new method for the dynamic signature verification based on the stable partitions of the signature. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2015. LNCS, vol. 9120, pp. 161–174. Springer, Heidelberg (2015)

    Chapter  Google Scholar 

  98. Zalasiński, M., Cpałka, K., Hayashi, Y.: New method for dynamic signature verification based on global features. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2014, Part II. LNCS, vol. 8468, pp. 231–245. Springer, Heidelberg (2014)

    Chapter  Google Scholar 

  99. Zalasiński, M., Cpałka, K., Hayashi, Y.: New fast algorithm for the dynamic signature verification using global features values. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2015. LNCS, vol. 9120, pp. 175–188. Springer, Heidelberg (2015)

    Chapter  Google Scholar 

Download references

Acknowledgment

The project was financed by the National Science Centre (Poland) on the basis of the decision number DEC-2012/05/B/ST7/02138.

Author information

Authors and Affiliations

  1. Institute of Computational Intelligence, Częstochowa University of Technology, Częstochowa, Poland

    Krystian Łapa & Krzysztof Cpałka

  2. Nanyang Technological University Singapore, Singapore, Singapore

    Lipo Wang

Authors
  1. Krystian Łapa
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Krzysztof Cpałka
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Lipo Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Krystian Łapa .

Editor information

Editors and Affiliations

  1. Częstochowa University of Technology, Czestochowa, Poland

    Leszek Rutkowski

  2. Częstochowa University of Technology, Czestochowa, Poland

    Marcin Korytkowski

  3. Częstochowa University of Technology, Czestochowa, Poland

    Rafał Scherer

  4. AGH University of Science and Technology, Krakow, Poland

    Ryszard Tadeusiewicz

  5. University of California, Berkeley, California, USA

    Lotfi A. Zadeh

  6. University of Louisville, Louisville, Kentucky, USA

    Jacek M. Zurada

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this paper

Cite this paper

Łapa, K., Cpałka, K., Wang, L. (2016). New Approach for Interpretability of Neuro-Fuzzy Systems with Parametrized Triangular Norms. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L., Zurada, J. (eds) Artificial Intelligence and Soft Computing. ICAISC 2016. Lecture Notes in Computer Science(), vol 9692. Springer, Cham. https://doi.org/10.1007/978-3-319-39378-0_22

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-39378-0_22

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-39377-3

  • Online ISBN: 978-3-319-39378-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation